Numerical methods for multivariate highly oscillatory integrals

In this paper, new algorithms are proposed for numerical evaluation of multivariate highly oscillatory integrals having critical point(s) over piecewise smooth rectangular and non-rectangular domains. Multi-resolution analysis is used to take care of the critical point(s). Theoretical error bounds o...

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Bibliographic Details
Published in:International journal of computer mathematics 2018-05, Vol.95 (5), p.1024-1046
Main Authors: Siraj-ul-Islam, Zaman, Sakhi
Format: Article
Language:English
Subjects:
65GXX
65Mxx
65Txx
65Yxx
Algorithms
Critical point
hybrid and Haar functions
Integrals
meshless collocation method
Multivariate highly oscillatory integrands
Numerical methods
stationary and resonance point(s)
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Summary:In this paper, new algorithms are proposed for numerical evaluation of multivariate highly oscillatory integrals having critical point(s) over piecewise smooth rectangular and non-rectangular domains. Multi-resolution analysis is used to take care of the critical point(s). Theoretical error bounds of the component methods of the new algorithms are found. Accuracy of the proposed algorithms is validated numerically on benchmark tests. Numerical results are compared with the methods available in the literature to ascertain stable and accurate performance of the new algorithms.
ISSN:0020-7160
1029-0265
DOI:10.1080/00207160.2017.1322202